% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/variation.R
\name{variation}
\alias{variation}
\title{Robust and classical variation matrix}
\usage{
variation(x, method = "robustPivot")
}
\arguments{
\item{x}{data frame or matrix with positive entries}

\item{method}{method used for estimating covariances. See details.}
}
\value{
The (robust) variation matrix.
}
\description{
Estimates the variation matrix with robust methods.
}
\details{
The variation matrix is estimated for a given compositional data set.
Instead of using the classical standard deviations the miniminm covariance estimator
is used (\code{\link[robustbase]{covMcd}}) is used when parameter robust is set to TRUE.

For method \code{robustPivot} forumala 5.8. of the book (see second reference) is used. Here 
robust (mcd-based) covariance estimation is done on pivot coordinates. 
Method \code{robustPairwise} uses a mcd covariance estimation on pairwise log-ratios.
Methods \code{Pivot} (see second reference) and \code{Pairwise} (see first reference) 
are the non-robust counterparts. 
Naturally, \code{Pivot} and \code{Pairwise} gives the same results, but 
the computational time is much less for method \code{Pairwise}.
}
\examples{

data(expenditures)
variation(expenditures) # default is method "robustPivot"
variation(expenditures, method = "Pivot")
variation(expenditures, method = "robustPairwise")
variation(expenditures, method = "Pairwise") # same results as Pivot

}
\references{
Aitchison, J. (1986) \emph{The Statistical Analysis of
Compositional Data} Monographs on Statistics and Applied Probability.
Chapman \& Hall Ltd., London (UK). 416p.

#' Filzmoser, P., Hron, K., Templ, M. (2018) \emph{Applied Compositional Data Analysis}.
Springer, Cham.
}
\author{
Karel Hron, Matthias Templ
}
\keyword{multivariate}
\keyword{robust}